I believe we should stop referring to this as a flag burning amendment. Under this wording,
"The Congress shall have power to prohibit the physical desecration of the flag of the United States,"
Congress would have wide leeway to name a number of different activities beyond burning to be desecration. They could make it illegal to have it raised at night unilluminated or make it illegal for it be out in the rain. Both are currently part of the US Flag code.
Pity the guy who puts in some overtime and finds the police on his doorstep when he arrives home after dark.